Current efforts towards the construction of a theory of quantum gravity reconciling general relativity and quantum mechanics are at crossroads: in spite of a huge collective intellectual effort over more than 40 years it looks like we may still be far from a final answer. In this talk I will give an overview of different approaches to the problem, and discuss their respective merits, problems and future perspectives.

Following up on Hermann Nicolai’s overview of the various approaches to quantum gravity and their current status, I present an inquiry into the historical origins of this diversity. Rather than focusing on  specific programs, I investigate three main historical processes of division: The emergence of different formalisms for constructing a quantum theory (quantization procedures), the different attitudes toward the role of quantum gravity within physics (final theory or mere consistency check), and the emergence of different specialized communities within the discipline of physics in the course of the twentieth century (in particular the establishment of the high-energy and general relativity/gravitation communities in the 1950’s). I conclude with some reflections on how an understanding of the origins of these divisions and the original arguments can help physicists in assessing the current status of quantum gravity.

Unitarity is an important property for the quantum states of a closed system, because it guarantees the conservation of probability. In my talk, I discuss unitarity in quantum gravity, where there is no longer an external spacetime. My discussion is divided into two parts. In the first part, I discuss the necessity to introduce fictitious ghost fields in the path-integral formulation of quantum gravity, which is also relevant for other theories such as Yang-Mills theories. In the second part, I address the fate of unitarity in quantum geometrodynamics, which is the non-perturbative canonical approach to quantum gravity in metric variables. This fate of unitarity is directly connected with the concept of time at the most fundamental level.

In the late 1940s, when renormalization methods were successfully applied in quantum electrodynamics, the community of quantum field theorists split into two groups. One group wanted to find a more solid ground for the theory, while the other group began to apply those new methods to other interactions, e.g., the nuclear and the gravitational ones. The latter group expected that these interactions could be handled with similar methods, however in the 1950s and 1960s such an expectation was frustrated. The gravitational field was particularly problematic, since it led to a non-unitary S-matrix, as Richard Feynman discovered in 1962. 

In this talk I will present a history of some quantum theories of the gravitational field from 1950 to 1967, emphasizing in particular the works of Richard Feynman, Bryce DeWitt, Ludwig Faddeev, and Victor Popov. I will explain their research projects and their main results—in particular the discovery, due to these four physicists, that, in order to restore the S-matrix unitarity, one must incorporate in the theory a new field, which is nowadays known as the Faddeev-Popov ghost. I will conclude with an epistemological reflection about the strategies for theory selection and about the role of mathematics in quantum gravity. 

The problem of observables and their supposed lack of change has been significant in Hamiltonian quantum gravity from the 1950s till now.  This talk considers the unrecognized variety of ideas about observables in the thought of constrained Hamiltonian dynamics co-founder Peter G. Bergmann, who also trained many students at Syracuse University, New York.  Whereas initially Bergmann required a constrained Hamiltonian formalism to be mathematically equivalent to the Lagrangian formalism, in 1953 Bergmann and Schiller introduced a novel postulate, motivated by facilitating quantum gravity.  This postulate held that observables were invariant under transformations generated by each individual first-class constraint.  While modern works rely on Bergmann’s authority, he had much to say about observables (e.g., 1953, 1956, 1956, 1957, 1961, 1962, 1962), not all mutually consistent and much of it rarely read.

On occasion he required observables to be locally defined (contrary to the inference that Bergmann's observables are changeless and global); at times he wanted observables to be independent of the Hamiltonian formalism (contrary to the definition involving separate first-class constraints).  Hence there is no concept of “Bergmann observables” (pace the physics literature) which he reliably endorsed.  A revised definition of observables that is coherent, is physically reasonable, and satisfies the requirement that equivalent theories should have equivalent formalisms can be devised with help from Bergmann (assisted by insights from others).  It implies that observables vary locally and are independent of the Hamiltonian formalism, as Bergmann sometimes wanted.

In this presentation, I use the development of the Chew and the Nambu-Jona-Lasinio models during the 1950s and 1960s as case-studies to illustrate the increasingly important role that approximation methods came to play in high-energy physics after WWII. After that, I go on to add some reflections on the kind of conceptual structures that are best suited to analyze the practice of high-energy physics during this period. The presentation is based on collaborative work carried out in the context of the Max Planck Research Group “Historical Epistemology of the Final Theory Program" together with Alexander Blum, James Fraser, and Rocco Gaudenzi.

The so-called Copenhagen interpretation provided a pragmatic, even if controversial, description of the ontological status of the wave function and of the role of Born's rule in quantum mechanics. In contrast the so-called de Broglie-Bohm interpretation, which lies at the foundation of the modern pilot-wave theory, offers a very different, and sometimes claimed more convincing, picture of reality. There is no doubt, from a historical point of view, that pilot-wave theory had a severe stop in 1927, i.e. after that the fifth Solvay conference took place in October. As a consequence, it gained the status of viable alternative only after the Fifties and it seems that its possible application to unsolved problems of Physics, like e.g. the search for quantum gravity, has emerged only recently. As we have already suggested in a previous paper, a recent historical analysis of the fifth Solvay conference showed how the first attempt to unify general relativity and wave mechanics, published by Léon Rosenfeld soon before the Solvay conference, was considered by Louis de Broglie as a possible implementation of his ideas. This paper aims to reconsider the work of Rosenfeld from this perspective and to clarify the role played by Theophile De Donder in the formulation of Rosenfeld's attempt. We argue that, in his earliest papers, Rosenfeld presented a pilot-wave approach to the problem of semiclassical quantum gravity. He considered the quantum behaviour of a many-particle system in a given gravitational and electromagnetic field and discussed both the role that could play gravity in de Broglie’s picture and the emergence of deterministic statistical interpretation, which agreed with Born’s rule. This was the highest point reached by pilot-wave theory before his stop between the end of Twenties and Bohm's revival. 

Black to white hole bounces are a class of quantum gravitational scenarios describing late stages of the lifetime of an evaporating black hole, under which presence of repulsive quantum effects leads to tunneling of the black geometry into a time-reversed solution (a white hole). Such bounces provide a form of singularity resolution as well as an answer to the information loss paradox. However, both the remnant proposals and white hole spacetimes are plagued by instabilities. It turns out that there are two distinct arguments for the white hole instability: an early argument based on infinite blueshift, and (arguably more compelling) an argument based on accretion. Some recent claims concerning the stability of white hole remnants address the infinite blueshift argument, but not the accretion argument. Attention to this detail implies corrections to the bounce scenario; I will illustrate this claim using an evaporating black hole embedded in a cosmological model with accelerating expansion.